JPS6120875B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to a musical tone synthesis method for electronic musical instruments and the like, and more particularly to a musical tone synthesis method that can continuously change the overtone structure (spectrum) of the resulting musical sound waveform, that is, the timbre. Various methods have been proposed to synthesize musical tones for electronic musical instruments. One of them is the one shown in U.S. Pat. No. 3,809,786 (Japanese Patent Application Laid-open No. 48-90217) called "computer towel gun". This is a method of synthesizing musical tones by calculating each Fourier component (each overtone) individually and summing them, and while it is effective in widening the range of musical tones that can be synthesized, it requires a large number of calculation circuits. Therefore, there is a drawback that the scale of the device configuration becomes large. Additionally, when increasing the number of harmonics used for musical tone synthesis, expand the harmonic coefficient memory to increase the number of harmonic coefficients, and increase the frequency of the calculation clock to shorten the harmonic calculation time interval. It is accompanied by technical difficulties. Alternatively, in order to increase the number of harmonics while fixing the frequency of the calculation clock, it is necessary to introduce a parallel processing method and greatly expand the scale of the device. Another method uses a frequency modulation method as disclosed in U.S. Pat. This method can generate many partial tones or overtones by calculating simple mathematical formulas, so it has the effect of compensating for the drawbacks of the Fourier component synthesis method described above, and it can be used to generate percussion instrument sounds (including piano) and wind instrument sounds. Effective for synthesis. However, on the other hand, when the modulation index ( ) is increased, the amplitudes of each part become uneven. That is, it has the disadvantage that significant irregularities occur in the spectral envelope, which is particularly inconvenient when trying to obtain a sound with a relatively smooth spectral distribution (for example, a string-type sound). This invention was made in view of the above points,
The present invention aims to provide a musical tone synthesis method that can continuously control the overtone structure of a musical sound waveform with a simple configuration. In this invention, when reading a waveform from a memory that stores a predetermined waveform (for example, a sine wave), the waveform amplitude value read from the memory is fed back to the input side that specifies the address of the memory at an appropriate feedback rate. By modulating the read address, a waveform with a desired spectral distribution is obtained from the output side of the memory. The spectral distribution of the obtained musical waveform can be controlled freely and continuously by changing the feedback rate, and therefore the overtone structure can be controlled by performing musical tone synthesis using the waveform obtained at the output side of the waveform memory. It is possible to obtain a musical sound waveform that can be continuously controlled. That is, in the first aspect of the present invention, in a musical tone synthesis method, a musical tone is synthesized by reading out a waveform memory storing data of a predetermined waveform using an address signal of a desired repetition frequency.
The output of the waveform memory is weighted by a parameter, the address signal of the waveform memory is modulated according to the weighted output, the memory is read out, and a musical tone is generated using the output of the waveform memory or the weighted output. In a second aspect of the present invention, a musical tone synthesis method comprises: The output of the waveform memory is weighted by a first parameter, the address signal of the waveform memory is modulated according to the weighted output to read the memory, and the weighted output is weighted by a second parameter. further weighting to obtain a second weighted output, modulating another address signal according to this second weighting output, and modulating a second weighted signal by this modulated another address signal. The third waveform memory is configured to read out a waveform memory and synthesize musical tones from the output read out from the second waveform memory.
In the invention, in a musical tone synthesis method for synthesizing musical tones by reading out a waveform memory storing data of a predetermined waveform using an address signal of a desired repetition frequency, the output of the waveform memory is used as a first parameter. and read out the memory by modulating the address signal of the waveform memory according to the weighted output, and weighting the output of the waveform memory by a second parameter separately from the above. A second weighted output is obtained, another address signal is modulated according to this second weighted output, a second waveform memory is read by this modulated another address signal, and this A musical tone is synthesized from the output read from the second waveform memory, and in the fourth invention, the waveform memory storing data of a predetermined waveform is read out using an address signal of a desired repetition frequency. In a musical tone synthesis method for synthesizing musical tones, the output of the waveform memory is weighted by a parameter, and the address signal of the waveform memory is modulated according to the weighted output to read out the memory. Equipped with multiple
modulating another address signal according to the waveform memory output of each series, and reading another waveform memory using the modulated another address signal;
A musical tone is synthesized from the output read from this separate waveform memory, and in the fifth invention, the waveform memory storing data of a predetermined waveform is read out using an address signal of a desired repetition frequency. In the musical tone synthesis method, the output of the waveform memory is weighted by a parameter, the address signal of the waveform memory is modulated according to the weighted output, and the memory is read out. The averaging means inserted at the output side of the waveform memory is configured to sequentially find the average value of the amplitudes of adjacent sample points of the musical tone waveform. Hereinafter, the present invention will be explained in detail based on the embodiments shown in the accompanying drawings. FIG. 1 is a block diagram showing the basic configuration of the present invention. The arithmetic unit 10 comprises an adder 11 and a sine wave memory 12 read out by the output y of the adder 11. A variable x as a phase input is added to one input of the adder 11, and the readout output sin_y of the sine wave memory 12 is fed back to the other input at an appropriate feedback rate. This feedback rate is set by the regression parameter β. That is, a multiplier 13 is inserted into the feedback loop, and multiplies the read output sin y of the memory 12 by the regression parameter β,
The product “β·sin y” is input to the adder 11. The output y of this adder 11 becomes x+βsin y, and this value becomes the actual address input to the sine wave memory 12. It is assumed that a predetermined delay time exists from the application of the input of the adder 11 to the output of the sine wave memory 12. The variable x is generated, for example, by the configuration shown in FIG. A signal representing a key pressed on the keyboard is supplied from the key logic 14 to a frequency number memory 15, from which a constant (frequency number or phase increment number) corresponding to the frequency of the pressed key is read out. The frequency numbers read from memory 15 are applied to accumulator 16, where they are repeatedly added in accordance with clock pulse φ. The accumulator 16 is a modulo M counter, and its output is the first variable x that specifies the phase.
The signal is supplied to the adder 11 shown in the figure. Here, M=2 ^N
(N is an integer), and the value of the variable x is the phase -π
-2 ^N-1 corresponding to +2 ^N corresponding to phase +π
The increase up to ^-1 is repeated at a predetermined frequency. Therefore,
The larger the frequency number, the faster the variable x increases, and the smaller the frequency number, the slower it increases. The repetition frequency of this variable x determines the frequency of the musical sound waveform obtained from the calculation unit 10 (FIG. 1). Musical sound waveform sin y obtained from the calculation unit 10
is produced through a circuit as shown in FIG. 3, for example. The envelope generator 17 generates an envelope waveform signal based on the key-on signal KON provided from the key logic 14 in response to a key press, and supplies it to the multiplier 18. In the multiplier 18, the musical sound waveform sin given from the arithmetic unit 10
Multiply y by the envelope waveform signal to obtain the musical sound waveform.
Controls the amplitude envelope of sin y. Multiplier 1
The musical tone signal outputted from 8 is applied to an output unit 19, and after being subjected to filtering and other appropriate processing, it is produced. In the configuration shown in FIG. 1, by changing the value of the regression parameter .beta., it is possible to continuously control the overtone structure of the musical sound waveform obtained from the arithmetic unit 10. The reason for this will be explained below. In the following description, it is assumed that there is no delay time included in the feedback loop to simplify the analysis. The phase input y of the obtained musical waveform sin y is the output of the adder 11, and is a function as shown below. y=x+β・sin y…(1) The musical sound waveform obtained as a result of the analysis of equation (1)
It was confirmed that sin y can be expressed as follows. This equation (2) can be expanded as follows. sin y=2/βJ ₁ (β)sin x+2/2βJ ₂ (2β)si
n2x +2/3βJ ₃ (3β) sin3x + (3) Here, Jn (nβ) is a Betzel function with n as the order and nβ as the modulation index. This formula is similar to the formula for a normal frequency modulation method in that it includes the Betzel function, but the Betzel function Jn (n
They differ significantly in that the order n is incorporated into the modulation index nβ of β), and that 2/nβ is multiplied as a coefficient of the Bessel function Jn(nβ). In equation (2) or equation (3), the fundamental wave component is found when n=1. The value of n corresponds to the order of each overtone component. If the relationship between the order of each overtone component and its relative amplitude is determined from Equation (2), it will be as shown in Table 1 below.

[Table] The spectral distribution shown in Table 1 above is
Let's analyze it from the three-dimensional diagram of the Betzel function Jn() shown in the figure. In the conventional musical tone synthesis method using frequency modulation, the component Jn of each order (n = 0, 1, 2,...)
Since the modulation index was common to (),
Each Betzel function value Jn() specified as a value (height) on a straight line that crosses the position of each order n in FIG. 4 at the position of a common modulation index determines the spectral distribution. Therefore, when is large, the resulting spectral envelope becomes wavy and uneven, and the spectral distribution becomes smooth (monotonic).
Control is difficult. However, in this invention, the modulation index nβ is
It increases monotonically in proportion to n. Therefore, the Bessel function Jn (nβ) obtained from FIG. 4 for each order n with =nβ is involved in determining the spectral distribution. This Betzel function Jn(n
In FIG. 4, β) is specified by a value (height) on a straight line passing through the origin of n=0, β=0 and having a gradient determined by β. This state is shown below the three-dimensional view of FIG. 4, superimposed on the three-dimensional view. This straight line rotates from the n-axis toward the axis as β changes from 0 to a larger value. As can be seen from FIG. 4, in the region 21 where 0≦β≦1 and the region 22 where β is somewhat larger than 1,
The spectral envelope represented by Jn(nβ) shows a monotonous tendency. That is,
The amplitude tends to become smaller as the order n becomes higher, and as the value of β becomes smaller, the amplitude gradually becomes smaller starting from higher-order components, and the spectral distribution tends to change smoothly. Of course, the true spectral distribution according to the present invention is somewhat different from that which can be read from the stereogram of FIG. This is because the Betzel function Jn(nβ) is multiplied by the coefficient 2/nβ. This makes the tendency for the amplitude to become smaller as the order n becomes higher. Now, if we proceed further with the analysis of the amplitude coefficient 2/nβJn (nβ) in equation (2), we will find that when the value of β is around 1,
It can be seen that the spectrum distribution is close to a sawtooth wave. For example, Betzel function Jn when β=1
When the value of (nβ) is determined from the Betzel function table, it is as shown in the following table.

[Table] As can be seen from Table 2, when β=1, the value of the Betzel function Jn (nβ) tends to be almost uniform regardless of n. When an approximate value of the amplitude coefficient 2/nβJn (nβ) is calculated from this, it shows a tendency as shown in the following table.

[Table] In other words, since Jn(nβ) is almost uniform regardless of n, 2/βJn(nβ) is considered to be the same even if n changes, and the amplitude coefficient is determined by the remaining coefficient 1/n. Almost fixed. The amplitude distribution shown in Table 3 corresponds to the spectral distribution of the sawtooth wave. Although Table 3 above is only an approximation, based on its tendency, if the configuration in Figure 1 is used, β=
It can be seen that when the value is 1, a musical sound waveform close to the spectral distribution of a sawtooth wave can be obtained. When the value of β is around 0 to 1, the Betzel function Jn (nβ) in which the order n is incorporated into the modulation index shows a tendency to increase almost monotonically. Therefore, when the value of β is around 1, Jn(nβ)
The value of shows a nearly uniform tendency regardless of the value of n,
A spectral distribution close to a sawtooth wave can be obtained. However, as β approaches 0 from 1, the Betzel function value Jn(nβ) for each order n gradually decreases, and the slope of decrease in Jn(nβ) becomes steeper for higher orders. This tendency can be easily confirmed from the Betzel function table. For example, β
Jn obtained from the Betzel function table when 0.1 and 0.5
The values of (nβ) are shown in Table 4.

[Table] In other words, the value of Jn (nβ) at β=0.5 becomes approximately 1/2 each time the order increases by one. Also,
The value of Jn (nβ) at β=0.1 becomes approximately 1/10 each time the order increases by one. Therefore, as β is gradually decreased from around 1 toward 0, the amplitude of the harmonic components gradually decreases, and the harmonic components tend to disappear in order of higher order. As described above, by changing the value of the regression parameter β within a certain range (from 0 to a number moderately larger than 1, for example up to 1.5), it is possible to smoothly control the amplitude of the constituent overtones of a musical sound waveform. I know what I can do. In the case of the configuration shown in Figure 1, β is large (1
If the value of β is gradually reduced, the amplitude gradually decreases from high order and the high order components gradually disappear.If β = 0, then a sawtooth wave can be obtained. The resulting musical sound waveform is a sine wave. Note that when β = 0, the feedback rate is 0, so the sine wave as stored in the memory 12 is obtained as a musical sound waveform, but if this is analyzed from the above equation (2), the fundamental wave component The amplitude coefficient of

[Formula] and other components The amplitude coefficient is

It is clear from the following formula. The above-mentioned matters have been confirmed using a prototype device. 5A to 5H show waveforms observed at various parts of FIG. 1 using the prototype device, and FIGS. 6A to 6H are graphs showing the spectral distribution of the obtained musical sound waveforms. These figures show regression parameter β values from 0.0982 to
Observation data for eight types of cases up to 1.571 are shown. In FIG. 5a, the first stage shows the observed waveform of the variable x, the second stage shows the observed waveform of the feedback amount β・sin y output from the multiplier 13, and the third stage shows the observed waveform of the feedback amount β・sin y output from the multiplier 13. The observed waveform of the output y is shown, and the fourth
The third row shows the observed waveform of the output sin y of the sine wave memory 12 read out by this y. The spectral distribution in Figure 6 is the output musical sound waveform of this memory 12.
This shows the overtone composition of sin y. Note that the repetition frequency of the variable x is 200Hz. Moreover, since the waveform of the variable x does not change even if β changes, it is shown only in FIGS. 5a and 5e, and the rest is omitted. From Figures 5 and 6, by changing the value of the regression parameter β, it is possible to continuously and smoothly control the number of overtones and their amplitudes of the synthesized musical waveform, from a sine wave to a sawtooth wave. It can be confirmed that it can change continuously. Next, with reference to FIG. 5, the tone synthesis effect in the configuration shown in FIG. 1 will be analyzed. First, when the value of the regression parameter β is a small value near 0, the feedback waveform β·sin y obtained through the multiplier 13 changes only slightly around 0. Therefore, the variable x is only slightly modulated in the adder 11, and the output y of the adder 11 and the variable x are similar. Therefore, a waveform close to the sine wave waveform stored in the memory 12 is obtained from the arithmetic unit 10 as the output musical waveform sin_y. This means that β
=0.0982 can be observed from the waveform diagram. As the value of regression parameter β increases,
The positive/negative swing of the feedback waveform β・sin y becomes noticeable. For example, if you look at the waveform diagram for β=0.3927, you can clearly see this. Then, the part of the variable x from -π to 0 is subtracted by the negative amplitude of the feedback waveform β·sin y, and the part from 0 to π is added by the positive amplitude of β·sin y. Therefore, when the amplitude of the feedback waveform β・sin y changes from negative to positive, the adder 11
The waveform of the output y tends to increase sharply. In the steep portion of the waveform y, the reading speed of the sine wave memory 12 becomes faster, and the slope of the portion where the amplitude of the read sine wave waveform rises from negative to positive becomes steep. The slope of the waveform y becomes gentle in areas other than steep parts, and correspondingly, the slope of the partial amplitude of the sine wave waveform read from the memory 12 also becomes gentle. In this case, the read waveform sin_y of the sine wave memory 12 becomes clearly different from the regular sine wave waveform. When the value of the regression parameter β further increases, the readout waveform sin y of the memory 12, which tends to have a steep slope rising from negative to positive, is fed back at a high rate, so that the output waveform y of the adder 11 This bias is further emphasized. Therefore, the musical sound waveform sin y read out from the memory 12 corresponding to y tends to become steeper when its amplitude changes from negative to positive, and becomes gentler when it changes from positive to negative.
Approaching a sawtooth wave. By the way, according to the inventor's experiment, the data was 10
As a bit, when the regression parameter β is made larger than approximately 1, the musical sound waveform output from the memory 12
It was observed that a hunting phenomenon as shown in Fig. 7a occurs in sin y. The part where this hunting phenomenon occurs is exactly in the vicinity where the value of the output data y of the adder 11 becomes the phase π (or -π). The reason why this hunting phenomenon occurs is thought to be due to errors in digital calculation. Looking at this hunting phenomenon, positive and negative amplitude data are repeatedly repeated at each output sample point of the memory 12. Therefore, an attempt was made to prevent the hunting phenomenon by using an averaging means having the configuration shown in FIG. The averaging means 23 includes a delay flip-flop 24 driven by a clock pulse φ that sets the sample point interval of the musical waveform, an adder 25 that adds the input and output of this flip-flop 24, and an output of the adder 25 that is 1/1. A multiplier 26 for multiplying by 2 is provided. This averaging means 23 is replaced by an adder 11,
It is inserted somewhere in the loop shown in FIG. 1 consisting of the memory 12 and the multiplier 13, and the adder 25 adds the data of the previous sample point delayed by the delay flip-flop 24 and the data of the current sample point. is multiplied by 1/2 in the multiplier 26, and the average value of the data of two adjacent sample points is determined. It is most effective to insert this averaging means 23 on the output side of the sine wave memory 12 (line 23' in FIG. 1). The averaging means 23 averages out the amplitudes that fluctuate in positive and negative directions for each sample point, thereby eliminating the hunting phenomenon. FIG. 7b shows the averaging means 2
This is the musical sound waveform observed when using 3, and hunting has been removed. The observed waveform in FIG. 5 was obtained by inserting an averaging means 23 at the line 23' in FIG. Furthermore, according to the prototype device, even if the repetition frequency of the variable x is increased (that is, even if the frequency of the musical waveform to be obtained from the calculation unit 10 is increased), the time of the steep part of the obtained sawtooth waveform remains almost constant. Something has been observed. This is the calculation unit 1 mentioned above.
This is due to a delay time of 0. In other words, the time delay of the calculation system is constant regardless of the frequency of the musical waveform to be obtained, but when the frequency is low,
Since the rate of progress is slow, this time delay is not a problem, and an ideal sawtooth wave with a steep rise can be obtained.
On the other hand, as the frequency increases, the progress of the variable x becomes faster, and the time delay of the calculation system cannot be ignored.
This appears as a delay in return. This causes the rising portion of the sawtooth wave to become dull. That is,
The time of the rising portion of the sawtooth wave does not become shorter in proportion to its period, and remains almost constant regardless of the frequency. As a result, as the frequency of the musical sound waveform increases, the higher harmonic frequencies are limited and the waveform becomes dull, which is convenient for removing aliasing noise that occurs due to the relationship with the sampling frequency. Although the memory 12 of the arithmetic unit 10 has been described as a sine wave memory that stores sine waves, the above-mentioned method is not limited to this, and even if a cosine wave or a sine function with an initial phase is stored. A similar effect can be obtained. Also, memory 1
It goes without saying that the waveform stored in 2 is not limited to a one-cycle waveform, but can be a half-cycle or a quarter-cycle waveform, and a known technique for controlling the readout of these waveforms to obtain a one-cycle waveform can be adopted. Next, another embodiment of the present invention will be described with reference to FIG. In FIG. 9, arithmetic units 10-1, 10
-2 has the internal configuration of the arithmetic unit 10 shown in Figure 1.
, and includes adders 11-1, 11-2 and sine wave memories 12-1, 12-2. 1st
The output sin y of the arithmetic unit 10-1 is multiplied by the regression parameter β in the multiplier 13-1 as in FIG. 1, and the product β·sin y is fed back to the input side.
Therefore, the first circuit including the multiplier 13-1 in the feedback loop
The operation of the arithmetic unit 10-1 is exactly the same as that shown in FIG. Feedback waveform β・sin obtained from multiplier 13-1
y is also given to the multiplier 27, and the modulation parameter m
is multiplied. The waveform signal mβ·sin y obtained from the multiplier 27 is applied to the adder 11-2 of the second arithmetic unit 10-2, and added to the variable _x1 .
The output Y of this adder 11-2 (=x ₁ + mβ・sin
The waveform sample point amplitude value is read out from the sine wave memory 12-2 in accordance with the value of y), and the output musical sound waveform is
Get sin Y. Variables supplied to first arithmetic unit 10-1
The variable x ₂ and the variable x ₁ supplied to the second arithmetic unit 10-2, like x in FIG. 1, is a phase input with a desired repetition frequency. The variables x ₁ and x ₂ may have the same repetition frequency or may be different. When the repetition frequencies of variables x ₁ and x ₂ are the same, the variable x obtained from the accumulator 16 of FIG.
It is sufficient to supply it in common to 0-2. i.e. x ₁ = x ₂
=x. In addition, if the repetition frequencies of variables x ₁ and x ₂ are to be different, as shown in Figure ₁₀ ,
x ₂ to form separately. That is, the first
The frequency number memory 15-1 and the second frequency number memory 15-2 store frequency numbers of different values for the same key, respectively, and the frequency numbers are stored in the frequency number memory 15-1 and the second frequency number memory 15-2, respectively, having different values for the same key. Different frequency numbers are stored in both memories 15-
Read from 1, 15-2. These frequency numbers are accumulated by accumulators 16-1 and 16-2 to obtain variables x ₂ and x ₁ with different repetition frequencies. The variable x ₂ output from one accumulator 16-1 is sent to the first arithmetic unit 10-1, and the variable x ₁ output from the other accumulator 16-2 is sent to the first arithmetic unit 10-1.
are supplied to the second arithmetic unit 10-2, respectively. The configuration of FIG. 9 includes a second arithmetic unit 10-2.
and m multiplier 27 perform frequency modulation. That is, the feedback waveform β sin y extracted from the middle of the feedback loop of the first arithmetic unit 10-1 is used as a modulating wave, and the repetition frequency of the variable x ₁ is used as a carrier wave frequency, which is set by the value of the modulation parameter m. Perform frequency modulation with modulation index. In this way, the second calculation unit 1
The spectral distribution of the musical sound waveform sin Y obtained from 0-2 can now be controlled by the regression parameter β and the modulation parameter m, and the range of control is expanded. When x ₁ = x ₂ = x, the second arithmetic unit 10-
Let us analyze the musical sound waveform sin Y obtained from 2. Adder 11-2 of second arithmetic unit 10-2
The output Y can be expressed as Y=x+mβsin y −(4). Here, sin y is the output of the first arithmetic unit 10-1. The musical sound waveform sin Y obtained as a result of the analysis of equation (4)
teeth,

[Formula] However, An=m[1/n+1-m・J _o+1 {(n+1-m)β} +1/n-1+m・J _o-1 {(n-1+m)β)]−(
5) It turns out that it can be expressed as Similarly to Equation (2) above, this Equation (5) also incorporates the order n in the modulation index of the Betzel function, and the denominator of the coefficient contains the order n, so the It can be inferred that the spectral distribution exhibits a tendency similar to that of equation (2). In other words, if the regression parameter β is set within a certain range (from 0 to a number moderately larger than 1), the spectral distribution of the resulting musical sound waveform (sin Y) will have a lower amplitude level as the order n increases. If the distribution exhibits a monotonically decreasing tendency and the value of β is varied within the above range, it is possible to continuously control the amplitudes of the constituent harmonics of the musical sound waveform. Therefore, even with the configuration shown in FIG. 9, string-type sounds (sawtooth wave-type sounds) can be easily synthesized, and the waveform shape can be controlled continuously from sine waves to sawtooth waves. can do. In FIG. 9, if x ₁ =x ₂ and m=1, the configuration will be the same as in FIG. 1. Therefore, x ₁ =x ₂ =x=
The observed waveforms and spectrum distribution diagrams of each part in FIG. 9 at 200 Hz and m=1 can be referred to those shown in FIGS. 5 and 6. If the value of the modulation parameter m is too small, it is not practical. For example, when m=0, the sine wave memory 12-2 of the second arithmetic unit 10-2 is read out by the variable _x1 (Y= _x1 ), and the resulting musical waveform
sin Y is a sine wave. According to the prototype device, interesting results were obtained when the value of the modulation parameter m was about 0.5 to 2. In Fig. 11 a to h and Fig. 12 a to h, x ₁ = x ₂ =
Figure 9 shows the observed waveforms and spectral distributions of various parts using the prototype device at 200Hz and m=2. These figures show the value of the regression parameter β.
Observation data for eight cases ranging from 0.0982 to 1.571 are shown. In the first stage of FIG. 11a, the variable x ₁ (=x ₂ ) is input to the second calculation unit 10-2.
The second stage shows the observed waveform of the feedback waveform β sin y output from the multiplier 13-1 in the feedback loop of the first arithmetic unit 10-1, and the third stage shows the observed waveform of Output Y of adder 11-2 of second arithmetic unit 10-2 (Y=x ₁ +mβsin y)
The fourth row shows the observed waveform of the musical sound waveform sin Y output from the second arithmetic unit 10-2. Note that the waveform of variable x ₁ does not change even if β changes, so it is shown only in Figure 11 a and e,
I omitted the rest. As is clear from FIG. 12, the configuration of FIG. 9 can also obtain a spectral distribution with the same tendency as the configuration of FIG. 1, and β can be varied in the range of 0 to about 1.5. It is confirmed that the spectral distribution can be controlled continuously. Moreover, when comparing FIGS. 11 and 12 with FIGS. 5 and 6, it can be seen that the former has more overtones and the level of each overtone is higher. Let's analyze this point by plotting Figure 13. Figure 13a shows the waveform for one period of the variable x ₁ , and m
The waveforms of the output Y (Y=x ₁ =mβsin y) of the adder 11-2 when =1, 2, 3, 4 are shown superimposed. Although the shape of this output Y varies depending on the value of β, it is assumed in FIG. 13 that β is fixed at an appropriate value. Figure 13b shows the sine wave memory 12-2.
1 shows a 1-cycle waveform of a sine wave stored in . FIGS. 13c and 13b schematically show the tone waveforms sin Y obtained when m=1, 2, and 3, 4. When m=1, the sine wave amplitude from 0 to π/2 is read out quickly, and the sine wave amplitude up to π/2 is read out slowly, so the musical sound waveform is as shown in Figure 13c.
sin Y becomes a sawtooth wave. When m=2, the sine wave amplitude from 0 to a phase close to π is read out quickly using the waveform Y shown in FIG. Therefore, as shown in FIG. 13c, the musical sound waveform Sin Y rises to a peak at the beginning of a half cycle, immediately falls near the 0 level, and thereafter gradually falls toward 0. Output Y of adder 11-2 when m=3 and 4
Since the phase exceeds the phase π, a negative amplitude is read out in the portion where the phase exceeds π. That is, when m=3, it is read quickly from 0 to π/2, through π to -π/2, and slowly from -π/2 to π (that is, -π). Therefore, as shown in Figure 13d, a musical waveform sin Y is obtained that rises to a positive peak at the beginning of a half cycle, immediately falls to a negative peak, and then slowly rises toward 0. . When m=4, from 0 to π/2, π(-π), -π/
One period of the sine wave is quickly read out from 2 to 0, and then slowly read out from 0 to -π/2 and further towards -π (π). Therefore, at the beginning of a half cycle, it rises to a positive peak, quickly falls to a negative peak, then quickly rises to near the 0 level, then slowly falls to the negative peak again, then slowly rises to the 0 level. An ascending musical sound waveform sin Y is obtained. From the above analysis, we can see that by increasing the value of the modulation parameter m in the configuration shown in Figure 9, it is possible to obtain a musical sound waveform sin Y with many high-order components, as if it were passed through a differential circuit or a high-pass filter. is confirmed. As described above, in the configuration of FIG. 9, changing the regression parameter β is involved in continuously controlling the spectral distribution, and increasing the modulation parameter m is useful for emphasizing the amplitude of higher-order components. Therefore, by appropriately adjusting the values of these parameters β and m, the tone color of the musical tone can be easily controlled. In the configuration of FIG. 9, if the repetition frequencies of the variables x ₁ and x ₂ are made different, a result somewhat different from the above analysis regarding the overtone structure can be obtained. As mentioned above, the frequency of the waveform sin y synthesized by the first arithmetic unit 10-1 is the same as the repetition frequency of the variable _x2 supplied to the first arithmetic unit 10-1. Therefore, from the multiplier 27 to the second arithmetic unit 10-
The frequency of the waveform mβsin y added to 2 is the variable x ₂
is the same as the repetition frequency of This allows the second
The musical sound waveform obtained from the calculation unit 10-2 of
The harmonic composition of sin Y will be the same as that obtained when the frequency corresponding to x ₁ is modulated by the frequency corresponding to x ₂ . As in the example in Figure 11, x ₁ =
When x ₂ , harmonics of all orders occur. However, the relationship between the repetition frequencies of variables x ₁ and x ₂ is 1:n
(However, when n is an integer of 2 or more), overtones of all orders are not generated, and overtones of a predetermined order are dropped. For example, if the relationship between the repetition frequencies of the variables x ₁ and x ₂ is set to 1:2, even-order harmonic components are dropped and the same spectral distribution as a rectangular wave can be obtained. FIG. 14 shows the observed waveform. Figures 14a to 14e show the results of the ninth test using the prototype device when the repetition frequency of x ₁ is 200 Hz, the repetition frequency of x ₂ is 400 Hz, and β is changed in five ways from 0.0982 to 1.571 when m = 1. The observed waveforms of each part of the figure are shown, and FIGS. 15a to 15e show the spectral distribution of the musical sound waveform sin Y shown in FIGS. 14a to 14e. In Figure 14, the waveforms of x ₂ and x ₁ are β
Since it does not change even if changes, it is shown only in Figure 14a and the rest is omitted. Further, FIG. 14 shows the feedback waveform β sin y and the waveform of the output tone waveform sin Y of the arithmetic unit 10-2. As is clear from the spectrum distribution diagram, even-order harmonic components are missing. The control characteristics by the regression parameter β are the same as in the other cases (Figures 5 and 6, Figures 11 and 12), and when the value of β is changed in the range from 0 to about 1.5, the number of overtones and amplitude gradually change. increase to Also,
The characteristics of the spectral distribution are also different in other cases (Fig. 5,
0), and shows a monotonous tendency in which the amplitude decreases as the higher-order components become higher. β
It can be seen that by setting it to 1.571, a waveform approximately equal to a rectangular wave is obtained. Further, as is clear from FIG. 14, by changing the value of β, the shape of the output musical sound waveform sin Y can be continuously varied and controlled from a sine wave to a rectangular wave. Note that if the relationship between the repetition frequencies of x ₁ and x ₂ is 1:2, it is not necessary to provide two frequency number memories 15-1 and 15-2 as shown in FIG.
As shown in Fig. 2, there is one series and an accumulator 16.
It is preferable to shift the output x to the left by one bit using a shift device to obtain 2x, and use this x and 2x as x ₁ and x ₂ . Alternatively, the repetition frequency of x ₁ may be made higher than the repetition frequency of x ₂ , and the relationship may be set to n:1 (where n is an integer of 2 or more). In this way, you can obtain interesting musical sound shapes. Furthermore, if the relationship between the repetition frequencies of x ₁ and x ₂ is a non-integer multiple, the spectral distribution of the musical sound waveform sin Y obtained from the arithmetic unit 10-2 will be composed of overtone components of non-integer multiples. , you can get non-harmonic sounds. It has also been confirmed that if the repetition frequencies of x ₁ and x ₂ are slightly different, a beat can be generated and a chorus effect can be obtained. In such a case, x ₁ and
It is good to generate x ₂ . In order to prevent the above-mentioned hunting phenomenon, the averaging means 23 shown in FIG. 8 is replaced with m in FIG.
It is assumed that it is inserted at an appropriate location such as the input side or output side of the multiplier 27 or the output side of the sine waveform memory 12-1. It is more effective to insert the averaging means 23 on the output side of the sine waveform memory 12-2. Next, still another embodiment of the present invention will be described with reference to FIG. 16. In FIG. 16, as in FIG. 9, adders 11-1, 11-2 and sine wave memories 12-1, 1
2-2, two arithmetic units 10-1 and 10-2 are provided. Further, the output sin y of the first arithmetic unit 10-1 is multiplied by a regression parameter β in a multiplier 13-1 and fed back to the input side. The difference from FIG. 9 is that the first arithmetic unit 1
The point is that the output sin y of 0-1 is applied to the input side of the second arithmetic unit 10-2 via the multiplier 28. The modulation parameter α is supplied to the multiplier 28, and αsin y is input to the adder 11-2 of the second arithmetic unit 10-2.
The adder 11-2 adds the variables x ₁ and αsin y to obtain Z=x ₁ +αsin y. This adder output Z
The sine wave memory 12-2 is read out, and the musical tone waveform sin Z is output. Arithmetic unit 10-
Variables x ₂ and x ₁ supplied to 1 and 10-2 respectively
is the same phase input as in Figure 9, and x ₁ =
It may be x ₂ or x ₁ ≠ x ₂ . In the configuration of FIG. 16, if β=α and the values of the regression parameter β and the modulation parameter α are set to be the same, the same state as when m=1 in FIG. 9 will be obtained. That is, αsin y=βsin y, Z=x ₁ +αsin y=x ₁ +βsin y=Y, and the resulting tone waveform is sin Z=sin Y,
The same tone waveform as the configuration shown in FIG. 9 is obtained. Therefore, the analysis of the tone waveform sin Z in this case is the same as in the case of FIG. If β=α and x ₁ =x ₂ , then FIG. 16 will be in the same state as the basic configuration of FIG. 1. The reason for this is the same as when x ₁ =x ₂ and m=1 in FIG. Furthermore, if α=mβ, then FIG. 16 will be in the same state as FIG. 9. Therefore, with the configuration shown in FIG. 16, it is possible to obtain the same tone waveforms as those obtained with the configurations shown in FIGS. 1 and 9. However, in the configuration of FIG. 9, the regression parameter β and the modulation parameter m are individually controlled, but the manner of controlling the parameters in the case of FIG. 16 is slightly different. However, if β and α are changed in conjunction so as to maintain the proportional relationship β∝α, the control becomes the same as the parameter control β∝mβ in FIG. That is, the control is exactly the same as when m is fixed and β is varied in FIG. 9. Therefore,
Said Fig. 5, Fig. 6, Fig. 11, Fig. 12, Fig. 1
The observed waveforms and spectrum distribution diagrams shown in FIGS. 4 and 15 can be used as they are as the observed waveforms and spectrum distribution diagrams of each part in FIG. 16. In other words, if we set x ₁ = x ₂ and β = α in Figure 16 and change β and α in conjunction, we can observe the same waveform as in Figures 5 and 6, and therefore the output musical waveform.
sin Z can be smoothly changed from a sine wave to a sawtooth. Also, in Figure 16, x ₁
If the interlocking control is performed to maintain the relationship β∝α with =x ₂ and α=2β, waveforms similar to those shown in FIGS. 11 and 12 can be observed. Furthermore, the variables x ₁ and x ₂
If the relationship of the repetition frequencies is 1:2, β=α, and the interlocking control is performed, waveforms similar to those shown in FIGS. 14 and 15 can be observed. Furthermore, in the configuration shown in FIG. 16, if the regression parameter β and the modulation parameter α are controlled independently, the constituent overtone components of the musical sound waveform sin Z can be controlled in a manner that could not be obtained with the configurations shown in FIGS. 1 and 9. can be done. Furthermore, when the regression parameter β is set to 0 and the feedback loop in the first arithmetic unit 10-1 is cut off,
The output waveform of the calculation unit 10-1 is sin y=
It becomes sin x ₂ , making it a sine wave. Therefore, the musical sound waveform sin Z obtained from the second calculation unit 10-2
is a waveform obtained by frequency-modulating a sine wave corresponding to the repetition frequency of variable x ₁ with a modulation degree α by a sine wave corresponding to the repetition frequency of variable x ₂ . As described above, according to the configuration shown in FIG. 16, by appropriately controlling the regression parameter β and the modulation parameter α, it is possible to produce tones (percussion instrument sounds and wind instrument sounds) that are good at conventional frequency modulation musical sound synthesis technology. It is possible to control a wide range of musical tones, from the tones that this invention is good at (for example, string tones). Of course, even in the configuration shown in FIG. 16, the averaging shown in FIG. Means 2
It is desirable to insert 3. FIG. 17 shows still another embodiment of the present invention, in which arithmetic units 10A and 10B having the same configuration as the arithmetic unit 10 of FIG. 1 and a multiplier 13 inserted in its feedback loop are used for multiplication. Vessel 13
Two combinations of A and 13B are provided in parallel. Arithmetic units 10A and 10B are separately supplied with phase input variables x _a and x _b of desired frequency, respectively. Furthermore, regression parameters β _a and β _b are supplied to multipliers 13A and 13B, respectively. The output waveforms of the arithmetic units 10A and 10B are applied to an adder 33, where they are added to a variable x (original address signal of the sine wave memory 34) of a desired frequency designated by a key press or the like. The sine wave memory 34 is read out by the output of the adder 33, and a musical waveform signal is obtained. That is, in FIG. 17, the address signal x is modulated by the output waveforms of the arithmetic units 10A and 10B, which operate in the same manner as the basic configuration shown in FIG. I am trying to read out the . In FIG. 17, if there is only one arithmetic unit (10A or 10B), the same state as in the case where the modulation parameter α is set to 1 in the configuration of FIG. 16 is obtained. Since the address signal x is modulated by the outputs of the plurality of arithmetic units 10A and 10B, a complex musical tone waveform is obtained from the sine wave memory 34, but as described above, the regression parameter β
By changing _a and β _b , the harmonic composition of the musical sound waveform is continuously controlled. Therefore, it is easy to control the tone waveform. Of course, the calculation units 10A and 10B
It is desirable to insert an averaging means 23 as shown in FIG. 8 on the output side of the . Further, although two arithmetic units 10A and 10B are used in FIG. 17, the present invention is not limited to this, and two or more arithmetic units may be used. In addition, in FIG. 9, FIG. 16, and FIG. 17, the calculation units 10-1, 10-2, 10A, 10B,
It is not necessarily required to use the multipliers 13-1, 13A, 13B, 27, and 28, respectively, but to provide them individually as specific devices. As shown in FIG. 18, it includes only one sine wave memory 30, one adder 31, and one multiplier 32, and further includes one register 20
It is also possible to have a control unit 29 and share these in a time-division manner. In this case, the control unit 29 executes the calculation procedure as shown in FIG. 9, FIG. 16, or FIG. 17 according to the program. The present invention is not limited to single-tone generation, but can also be applied to multiple-tone generation. In the case of multiple tones, the key logic 14 shown in FIG. 2 is constituted by a known sound allocating circuit called a key assigner or channel processor, and synthesizes tones assigned to each channel in a time-division manner. In addition, the regression parameter β and the modulation parameters m and α are expressed as time functions β(t), m(t), α(t)
It is also possible to do this. In this case, key logic 1
Based on the key-on signal KON applied from 4, an envelope generator (not shown) corresponding to each parameter β(t), m(t), α(t) is driven, and each parameter β(t), It is preferable that m(t) and α(t) be generated as envelope waveforms corresponding to key press operations (sounding time intervals). In the above embodiment, the range of the regression parameter β is from 0 to about 1.5, but other values can also be expected to produce effects different from the conventional ones. Furthermore, even if waveforms other than trigonometric functions are stored in the sine wave memory 12, different effects can be expected. In addition, with this invention, a waveform memory (sine wave memory 1
2) shall also include devices that generate waveforms through calculations. That is, a waveform memory includes a waveform generator that executes waveform amplitude calculation using an input corresponding to an address signal as a phase parameter. As explained above, according to the present invention, since the read waveform from the waveform memory is fed back to the address input side at an appropriate feedback rate, it is possible to read out a waveform different from the waveform stored in the memory.
Furthermore, the shape of the readout waveform can be changed by controlling the feedback rate using the regression parameter β. Specifically, waveforms such as sawtooth waves, square waves, or waveforms with emphasized high-order harmonic components can be easily obtained by simply controlling parameters, and the number of constituent harmonics can be varied from these waveforms to sine waves. and the amplitude can be controlled by continuously decreasing (or vice versa, continuously increasing). In particular, it is advantageous for synthesizing and controlling musical waveforms having a spectral distribution in which the amplitude of overtones tends to decrease as the order increases. Synthesizing musical tones with a monotonically decreasing spectral distribution in which the amplitude decreases as the order goes up is something that conventional frequency modulation musical tone synthesis technology is weakest at, and this invention has significantly improved this point. It has been improved. In addition, the number of overtones can be increased simply by changing the value of the regression parameter β without any special expansion of the scale of the device configuration, which overcomes the drawbacks of conventional Fourier component synthesis method musical tone synthesis technology. There is. Further, by modulating the address signal for reading out the second waveform memory using the waveform obtained from the waveform memory or a signal obtained by weighting the waveform with a predetermined weight as a modulating waveform, the second waveform memory can be read out. The output waveform has the above-mentioned characteristics but changes in a more complicated manner. Therefore, by synthesizing a musical sound waveform from this waveform, a musical tone that changes more complexly can be obtained. Further, it includes a plurality of series for weighting the output of the waveform memory according to parameters and reading out the memory by modulating the address signal of the waveform memory according to the weighted output. Therefore, if another address signal is modulated and another waveform memory is read using this modulated address signal, the output waveform read from this other waveform memory will become even more complex. By synthesizing musical tones from the output read from this separate waveform memory, musical tones with a wide variety of variations can be obtained. In this case as well, the overtone composition of the musical tone waveform is continuously controlled in accordance with changes in the regression parameter, as described above, and the musical tone waveform can be easily controlled.
Furthermore, by inserting an averaging means on the output side of the waveform memory, the amplitudes that touch positive and negative at each sample point are averaged, and the hunting phenomenon of musical tones can be eliminated.

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing the basic configuration of this invention, Fig. 2 is a block diagram showing an example of a device for generating the variable x used in Fig. 1, and Fig. 3 is a block diagram showing the output tone waveform of Fig. 1. FIG. 4 is a block diagram schematically showing an example of a device that performs processing and produces sound; FIG. Diagram a
- h are graphs showing the results of observing the waveforms of various parts in Fig. 1 for various β values using a prototype device, and Fig. 6 a - h are each musical sound waveform shown in Fig. 5 a - h.
A graph showing the observation results of the spectral distribution of sin y. Figure 7 is a graph showing an example of a waveform in which the hunting phenomenon has occurred and an example of a waveform from which it has been removed, based on the observation results with a prototype device. Figure 8 is a graph showing the observation results of the spectral distribution of sin y. A block diagram showing an example of averaging means for preventing the hunting phenomenon shown in the figure, FIG. 9 is a block diagram showing the configuration of another embodiment of the present invention, and FIG. 10 shows different variables x ₁ and x _{2 A} block diagram showing an example _of a device that generates Graphs showing the results, Fig. 12 a to h are graphs showing the observation results of each musical sound waveform sin Y shown in Figs. 11 a to h.
Figure 3 shows a diagram for analyzing by plotting the fact that when the value of the modulation parameter m is increased in the configuration shown in Figure 9, the output musical waveform tends to become a differential waveform with emphasized high-order harmonic components. Graph, 14th
Figures a to e show the results of observing the waveforms of each part in Figure 9 for various β values when the relationship between the repetition frequencies of the variables x ₁ and x ₂ is 1:2 and m = 1 using a prototype device. Graphs, FIGS. 15 a to 15 e are graphs showing the observation results of the spectral distribution of each musical sound waveform sin Y shown in FIGS. 14 a to e, and FIG. 16 shows the configuration of yet another embodiment of the present invention. FIG. 17 is a block diagram schematically showing still another embodiment of the present invention, and FIG. 18 is a block diagram showing still another embodiment of the present invention, in which a single arithmetic circuit is controlled by a program. FIG. 10,10-1,10-2,10A,10,B
...Arithmetic units, 11, 11-1, 11-2...
... Adder, 12, 12-1, 12-2 ... Sine wave memory, 13, 13-1, 13A, 13B, 2
7, 28... Multiplier, 21, 22... Preferred area of Betzel function values used in this invention.
23...Averaging means.

Claims (1)

[Claims] 1. A musical tone synthesis method in which a musical tone is synthesized by reading out a waveform memory storing predetermined waveform data using an address signal of a desired repetition frequency, the output of the waveform memory being controlled by a parameter. A musical tone synthesis method, in which the weighted output is added to an address signal of the waveform memory and the memory is read, and a musical tone is synthesized using the output of the waveform memory or the weighted output. 2. In a musical tone synthesis method in which a musical tone is synthesized by reading out a waveform memory storing predetermined waveform data using an address signal of a desired repetition frequency, the output of the waveform memory is overlaid by a first parameter. adding the weighted output to the address signal of the waveform memory to read the memory, and further weighting the weighted output by a second parameter to obtain a second weighted output; Add this second weighted output to another address signal and add this second weighted output to another address signal.
A second waveform memory is read out using another address signal to which a weighted output is added, and a musical tone is synthesized from the output read out from the second waveform memory. 3. In a musical tone synthesis method in which a musical tone is synthesized by reading out a waveform memory storing predetermined waveform data using an address signal of a desired repetition frequency, the output of the waveform memory is overlaid by a first parameter. The weighted output is added to the address signal of the waveform memory to read the memory, and the output of the waveform memory is weighted by a second parameter separately from the above to produce a second weighted output. is obtained, this second weighted output is added to another address signal, and the second waveform memory is read by another address signal to which this second weighted output is added. A musical tone synthesis method in which musical tones are synthesized from the output read from the waveform memory. 4. A musical tone synthesis method in which a musical tone is synthesized by reading out a waveform memory storing predetermined waveform data using an address signal of a desired repetition frequency, the output of the waveform memory being weighted by a parameter; and a plurality of series for reading out the memory by adding the weighted output to the address signal of the waveform memory, adding the waveform memory output of each series to another address signal, and adding the weighted output to the address signal of the waveform memory to read the memory. A musical tone synthesis method in which a separate waveform memory is read in response to an address signal, and a musical tone is synthesized from the output read from the separate waveform memory. 5. A musical tone synthesis method in which a musical tone is synthesized by reading out a waveform memory storing predetermined waveform data using an address signal of a desired repetition frequency, the output of the waveform memory being weighted by a parameter; The weighted output is added to the address signal of the waveform memory, the memory is read out, and the average value of the amplitudes of adjacent sample points of the musical waveform is sequentially determined by averaging means inserted on the output side of the waveform memory. A method of musical tone synthesis.